UCT-Kirchberg algebras have nuclear dimension one

By Efren Ruiz, Aidan Sims, Adam P. W. Sørensen. 2014

46 citations recorded by the source corpus.

We prove that every Kirchberg algebra in the UCT class has nuclear dimension 1. We first show that Kirchberg 2-graph algebras with trivial $K_0$ and finite $K_1$ have nuclear dimension 1 by adapting a technique developed by Winter and Zacharias for Cuntz algebras. We then prove that every Kirchberg algebra in the UCT class is a direct limit of 2-graph algebras to obtain our main theorem.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/74d79102a5581cdf2b1217aad779883f6082edde

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Stuart White
2. Rufus Willett
3. Aaron Tikuisis
4. Yasuhiko Sato
5. N. Brown
6. W. Winter
7. E. Guentner
8. Guoliang Yu

In Geometry and Topology

1. Stuart White
2. Rufus Willett
3. Aaron Tikuisis
4. Yasuhiko Sato
5. Guoliang Yu
6. N. Brown
7. J. Bosa
8. W. Winter

In Mathematical Physics

1. Rufus Willett
2. Stuart White
3. Aaron Tikuisis
4. W. Winter
5. Guoliang Yu
6. Yasuhiko Sato
7. N. Brown
8. E. Guentner

Citations in the corpus

• Dynamic asymptotic dimension: relation to dynamics, topology, coarse geometry, and $$C^*$$C∗-algebras (2015, background): “Note however that if ü X is a minimal, free, amenable action of a non-amenable group on the Cantor set, then C(X) r is a Kirchberg algebra in the UCT class; the main result of [34] (see also [5]) thus implies that the nuclear dimension of C(X) r is one.”
• Covering Dimension of C*-Algebras and 2-Coloured Classification (2015, methodology): “Indeed, all Kirchberg algebras have finite nuclear dimension [72, 40, 52], while no analogues of type II∞ factors (i.”